By a 52 to 45 vote, with Sen. Olympia Snowe, R-Maine, voting "present," the Senate fell eight votes short of the number needed to cut off the debate and move forward. Sen. Bill Nelson, D-Fla., voted for moving forward with debate.

Republicans objected because Democrats wanted to close a tax loophole to fund the plan. The House of Representatives has passed legislation to freeze the rate, which would double to 6.8 percent July 1 if nothing is done. But Democrats disliked the GOP-authored House plan because it cut money for health care.

Rubio took to social media to explain his vote, saying this on Twitter: "As maybe only Sen paying a #studentloan surreal listening to Dem colleagues lecture me on #studentloandebt."

Rubio said he supports "a hundred percent making sure that the interest rates on student loans do not go up," but doesn't support the Democratic plan.

He's not the only high-profile U.S. leader who's griped about about paying back the loans. It's also become a frequent refrain on the campaign trail for President Barack Obama and First Lady Michelle Obama.